M1837489 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	16.1709	68.6567%	500000	15000000	0.1015	5.0711%	16.2724	70.2462%	1.5894%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8813%	0.0117	64.2194%	1.0615%
GPU72	2⁶¹	0.1672	65.5738%	9000	140000	0.0013	1.5959%	0.1684	66.1232%	0.5494%
Difference	+6	+16.0038	+3.0829%	+491000	+14860000	+0.1002	+3.4751%	+16.1040	+4.1230%	+4.1230%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1709

68.6567%

500000

15000000

0.1015

5.0711%

16.2724

70.2462%

1.5894%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8813%

0.0117

64.2194%

1.0615%

GPU72

2⁶¹

0.1672

65.5738%

9000

140000

0.0013

1.5959%

0.1684

66.1232%

0.5494%

Difference

+16.0038

+3.0829%

+491000

+14860000

+0.1002

+3.4751%

+16.1040

+4.1230%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1837489	16754224703	11	33.964	4559 47 × 97	-	47	97	1.237e-9	3.911e-6	7.524e-6
1837489	2543757263899199	16	51.176	692182991 29 × 541 × 44119	2014-06-19	541	44119	0.0002	0.0002	0.0004
1837489	24920344060288302265647299969	29	94.331	6781086597059438795456 2⁶ × 13 × 761 × 1933 × 3259 × 1700102449	2020-05-27	3259	1700102449	3.174e+9	7.2865	13.609

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1837489

16754224703

33.964

4559
47 × 97

1.237e-9

3.911e-6

7.524e-6

1837489

2543757263899199

51.176

692182991
29 × 541 × 44119

2014-06-19

541

44119

0.0002

0.0004

1837489

24920344060288302265647299969

94.331

6781086597059438795456
2⁶ × 13 × 761 × 1933 × 3259 × 1700102449

2020-05-27

3259

1700102449

3.174e+9

7.2865

13.609

exponent	prime factors	composite factor	digits	bits*
1837489	16754224703 2543757263899199	42618680789255649987712897	26	85.140
1837489	16754224703 24920344060288302265647299969	417521044062141595121038861425870934207	39	128.295
1837489	2543757263899199 24920344060288302265647299969	63391306222225627220846855801451211331824831	44	145.507
1837489	16754224703 2543757263899199 24920344060288302265647299969	10620721886638502112231816280485527481449331136090 00193	55	179.471

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:40:20	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 16754224703 skipped known factor: 2543757263899199	-	-	0.101	-	-	5.071%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-06-19T11:32:00	TJAOI	Manual testing	?	?	2543757263899199	51.176	16	2.58312e-5	0.213	5.51512e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-06-19T11:32:00

TJAOI

Manual testing

2543757263899199

51.176

2.58312e-5

0.213

5.51512e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.237 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.237 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.575	0.019%
25	50000	0.777	45.986%
30	250000	0.048	95.308%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.280
50000	5000000	24920344060288302265647299969	3	0.207
50000	6600000		215	16.75

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-15T19:11:42	alpertron		50000	5000000						3	0.207
2018-09-28T16:54:55	alpertron	Manual testing	50000	5000000						3	0.207
2020-05-27T13:41:12	nordi	sweet16	50000	5000000	24920344060288302265647299969	94.331	3	2	2189915616914162	3	0.207
2020-06-23T12:41:31	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.207
2020-07-20T13:36:31	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-09-20T00:13:39	nordi	sweet16	50000	5000000						7	0.484
2020-11-24T09:04:17	nordi	sweet16	50000	5000000						7	0.484
2021-02-19T15:43:20	Kublenz	Medion_E4272	50000	5000000						7	0.484
2021-04-30T08:12:46	TJAOI	Manual testing	50000	6600000						215	16.75

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T03:09:48

Oliver Kruse

GTX-2

16754224703

2543757263899199

BF7DFBDB968D35__

2017-11-06T09:56:20

kkmrkkblmbrbk

c4.xlarge

16754224703

2543757263899199

BF7DFBDB968D35__

2020-05-27T13:51:57

ATH

ec2-PRPCF

16754224703

2543757263899199

24920344060288302265647299969

2E22285C888F9145

2020-06-06T11:00:08

oodaira

com2

16754224703

2543757263899199

24920344060288302265647299969

2E22285C888F9145

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront